A Low-Latency Collaborative HARQ Scheme for Control/User ... · capability of mobile equipments, it is difﬁcult to overcome the severe challenges in high-speed railway scenarios,

2282 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 17, NO. 8, AUGUST 2016

A Low-Latency Collaborative HARQ Scheme forControl/User-Plane Decoupled Railway

Wireless NetworksLi Yan, Student Member, IEEE, Xuming Fang, Member, IEEE, Geyong Min, Member, IEEE, and

Yuguang Fang, Fellow, IEEE

Abstract—The control/user (C/U) plane decoupled railway wire-less network is an innovative architecture recently proposed tomeet the communication demands of both train control systemsand onboard passengers. The core idea is to completely separatethe C-plane and the U-plane into different network nodes operat-ing at different frequency bands. Although the system capacity ofthis network architecture can be highly increased, the forwardinglatency of X3 interfaces to link the C-plane and the U-planebecomes a serious problem, particularly for hybrid automatic re-peat request (HARQ) protocols that demand frequent interactionsbetween the C-plane and the U-plane. To address this challengingproblem, we propose a low-latency collaborative HARQ schemein this paper. Specifically, we develop a new collaborative trans-mission framework where the possible spare resources on lowerfrequency bands of macrocells excluding those used by C-planetransmissions can be utilized to help small cells relay erroneouslyreceived data. Compared with the conventional HARQ scheme,the proposed scheme requires fewer retransmissions to reachthe same transmission reliability, thereby mitigating the latencyproblem caused by HARQ retransmissions. Furthermore, channelmapping is also redesigned to conform to the proposed collabo-rative transmission framework. Through theoretical analysis, wederive the expression of the average number of retransmissionsrelated to the sum of independent Gamma variables. Finally, theresults of simulation experiments show that the proposed schemecan largely decrease the retransmission latency for railway wire-less networks.

Index Terms—C-plane and U-plane decoupling, collaborativetransmission, low latency, HARQ, railway communications.

I. INTRODUCTION

R ECENT rapid developments of railway technologies andmobile Internet have stimulated increasingly pressing

demands on high-speed wireless access. However, no mobile

Manuscript received September 30, 2015; revised November 13, 2015;accepted January 11, 2016. Date of publication February 15, 2016; date ofcurrent version July 29, 2016. This work was supported in part by the 973Program of China under Grant 2012CB316100, by the National Natural ScienceFoundation of China under Grant 61471303, and by the EU FP7 QUICK projectunder Grant PIRSES-GA-2013-612652. The Associate Editor for this paperwas F.-Y. Wang.

L. Yan and X. Fang are with the Key Lab of Information Coding andTransmission, Southwest Jiaotong University, Chengdu 610031, China (e-mail:[email protected]; [email protected]).

G. Min is with the College of Engineering, Mathematics and PhysicalSciences, University of Exeter, Exeter EX4 4QF, U.K. (e-mail: [email protected]).

Y. Fang is with the Department of Electrical and Computer Engineering,University of Florida, Gainesville, FL 32611 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TITS.2016.2518189

network operators would provide full and dependable wirelesscoverage for sparsely-populated railway scenarios with low rev-enue return. Furthermore, due to the limited signal processingcapability of mobile equipments, it is difficult to overcomethe severe challenges in high-speed railway scenarios, such aslarge penetration loss, high mobility and fast group handovers[1]. As a result, a novel unified railway wireless network isurgently needed to meet the communication demands of bothtrain control systems and onboard passengers. To this end,industrial participants have reached the consensus that the cur-rent narrowband Global System for Mobile Communication forRailway (GSM-R) will evolve to Long Term Evolution (LTE)for railway communication systems in the near future [2], [3].In addition, a C/U-plane decoupled railway wireless networkwas proposed [4], [5]. To address the problems caused by thedirect connection between onboard passengers and waysidebase stations, an access point (AP) is deployed inside thetrain to collect passengers’ services in this network. Theseservices are then relayed to wayside base stations by a mobilerelay (MR) deployed on the roofs outside the train [1], [6].More importantly, a concept of decoupling C-plane and U-planeis applied to this network. To guarantee the transmission re-liability and coverage, the more important C-plane is kept inthe macro cells with relatively high-quality lower frequencybands, i.e., conventional 800 MHz ∼ 2 GHz frequency bands.In contrast, as the main data carrier, the U-plane needs moretransmission capacity, thereby being moved to small cells oper-ating at broadband higher frequency bands, including frequencybands higher than 5 GHz, up to 300 GHz. In [4], to provide abetter understanding of this network architecture, we studiedthe bandwidth matching between macro cells and small cells,where 96 passengers’ C-plane can be supported in a sub-frame with a bandwidth of 5 MHz in macro cells, and thecorresponding required bandwidth in small cells is 21.2 MHzwith a date rate of 500 Kbps per passenger. With more availablebandwidth in macro cells, more passengers can be served, andtherefore more bandwidth is required in small cells. Besides,as the data rate of passengers increases, the required band-width in small cells will also be enlarged. Considering morestringent requirements for transmission reliability, train controlinformation is entirely kept at macro cells without decoupling.Through a newly introduced interface, namely, X3, macro cellsand small cells can interact and synchronize with each other.From a purely technical point of view, X3 interfaces employ thesame protocols of traditional X2 interfaces in LTE networks [7].

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YAN et al.: HARQ SCHEME FOR CONTROL/USER-PLANE DECOUPLED RAILWAY WIRELESS NETWORKS 2283

Through retransmissions to ensure transmission reliability,the hybrid automatic repeat request (HARQ) protocol playsan important role in LTE networks [8]–[11]. However, inC/U-plane decoupled railway wireless networks, the C-planesignaling, including HARQ acknowledgments, is transmittedon relatively high-quality lower frequency bands, while theU-plane data are carried by higher frequency bands. In otherwords, the ACK/NACK message receiving and data transmit-ting of an HARQ process are in a macro cell and a small cell,respectively, not in the same network node. Therefore, macrocells need to forward the received HARQ acknowledgments tosmall cells via X3 to instruct small cells what to do next, andhandle retransmissions if the acknowledgement is an NACKor send new data if it is an ACK. Obviously, the decouplingC-plane and U-plane cause more overhead in X3. Since inthis paper we focus on the HARQ retransmission latency, theoverhead is taken into account in the form of forwarding latencyof X3 interfaces. According to the field test results in [12], theforwarding latency of X2 interfaces is about 1 ms on averageand 6 ms at maximum. Because X3 interfaces adopt the sameprotocols as X2 interfaces, the above results also apply toX3 interfaces. Consequently, the time interval between twoadjacent (re)transmissions of an HARQ process in C/U-planedecoupled railway wireless networks is enlarged. How to re-duce the aggravated latency of HARQ retransmissions in thisnetwork becomes a significant challenge.

In the conventional network architecture, C-plane andU-plane share the same frequency resources in macro cells.The available resources for the C-plane in LTE networks arevery limited because only the first three OFDM symbols in asubframe are used for control channels [11]. In contrast, in theC/U-plane decoupled railway wireless network, the resourcesof lower frequency bands in macro cells are all used for theC-plane. As a consequence, some relatively high-quality andspare spectrum resources may become available in macro cells,which could be further exploited to assist small cells to handleretransmissions, aiming at reducing the retransmission latency.To sum up, the main contributions and novelties of this paperinclude:

1) The timing of the conventional HARQ scheme underC/U-plane decoupled railway wireless networks is ana-lyzed to investigate how decoupling C-plane and U-planecan affect the retransmission latency of HARQ, demon-strating the critical issue of aggravating the latency prob-lem of HARQ in C/U-plane decoupled railway wirelessnetworks.

2) To reduce the HARQ retransmission latency in C/U-planedecoupled railway wireless networks, we propose a collab-orative HARQ scheme in which the potential spare lowerfrequency band resources in macro cells excluding thoseused for C-plane transmissions are exploited to help smallcells handle retransmissions. Furthermore, double copiesof data are concurrently transmitted in macro cells andsmall cells in the process of retransmission in order toreduce the total number of required retransmissions andthe retransmission latency. Accordingly, the timing of theproposed collaborative HARQ scheme is designed. Con-

sidering the significant difference of signal propagationbetween the lower and higher frequency bands, the processof data combining is studied from the hardware point ofview.

3) To determine how to realize collaborative retransmissionsbetween different network nodes in macro cells and smallcells, a collaborative transmission framework betweenmacro cells and small cells is proposed to reduce theaggravated latency and enhance the flexibility of band-width extension for C/U-plane decoupled railway wirelessnetworks. This framework can also be generalized tocommon U-plane data collaborative transmissions beyondrailway wireless networks. To this end, the channel map-ping is redesigned to conform to this framework.

4) For both the conventional and proposed schemes, weconduct theoretical analysis of the average number ofretransmissions related to the sum of independent Gammavariables. Based on the analytical results, the averagenumber of retransmissions, the average retransmission la-tency and the average transmission rate of the conventionaland proposed schemes are compared through numericalexperiments.

The remainder of this paper is organized as follows. InSection II, we describe the timing of the conventional HARQscheme applied to C/U-plane decoupled railway wirelessnetworks and present the aggravated retransmission latencyproblem. In Section III, the collaborative HARQ scheme tomitigate this problem is proposed. In Section IV, to enhance theflexibility of bandwidth extension of the C/U-plane decoupledrailway wireless networks, a general collaborative transmissionframework is proposed. In Section V, analytical results forthe average number of retransmissions related to the sum ofindependent Gamma variables are derived. In Section VI, sim-ulation results are illustrated and analyzed in details. Finally,conclusions are drawn in Section VII.

II. CONVENTIONAL HARQ SCHEME IN C/U-PLANE

DECOUPLED RAILWAY WIRELESS NETWORKS

This section presents the C/U-plane decoupled railway wire-less network architecture and then discusses the problems oftiming and aggravated retransmission latency of the conven-tional HARQ scheme working in this network architecture.

A. C/U-Plane Decoupled Railway Wireless Networks

In order to increase the system capacity to meet the wirelessaccess demands of train passengers, a C/U-plane decoupledrailway wireless network was proposed in [4], [5]. As shownin Fig. 1, an AP and an MR are deployed on the roofs insideand outside trains, respectively, so as to provide a dependableconnection for train passengers. The inside AP firstly collectsthe services of train passengers, and then these services areforwarded to the wayside base stations via the MR. In this way,the problems caused by the direct connection between onboardpassengers and wayside base stations, such as large penetra-tion loss, high mobility and group handovers, can be avoided.According to [1], backhaul links between MRs and wayside


Fig. 1. C/U-plane decoupled railway wireless networks.

base stations are the key capacity bottlenecks. Therefore, theC/U-plane decoupled architecture is applied to these links. Toenable efficient mobility support, the critical C-plane is kept inmacro cells operating at relatively high-quality lower frequencybands. The corresponding U-plane, which is the main datacarrier, is moved to broadband but relatively poor-quality higherfrequency bands to expand the system capacity. Specifically,some low-rate services with absolute demands on transmissionreliability, e.g., train control information, can be entirely dis-tributed to macro cells without decoupling. Since small cells areonly responsible for the U-plane without handling any controlfunctions, they are solely connected to the SGW, but not tothe MME as shown in Fig. 1. Via X3 interfaces, macro cellsand small cells can exchange control signaling and data as wellas synchronize with each other. In order to provide some low-rate services that have stringent requirements for transmissionreliability, in addition to the MME, macro cells can also beconnected to the SGW.

B. Timing of the Conventional HARQ in C/U-PlaneDecoupled Railway Wireless Networks

Stop and Wait (SaW) is a typical HARQ retransmissionmechanism where the next transmission is performed onlywhen the acknowledgment to the previous transmission isreceived [11]. To fully utilize the resources while waitingfor acknowledgments, multiple HARQ processes are carriedout. In the conventional network architecture, the number ofsynchronous HARQ processes in frequency division duplex(FDD) systems is eight, i.e., the maximum latency caused bya retransmission is 8 ms. While in the C/U-plane decoupledrailway wireless networks, the maximum latency of HARQ is8 + �Td,max�, where �Td,max� denotes the maximum forward-ing latency of X3 interfaces. According to the field test resultsin [12], the forwarding latency of X2 interfaces is about 6 msat maximum. Then, the time interval between two adjacent(re)transmissions of an HARQ process in this network is 14 ms,which is much larger than that of HARQ in the conventionalnetworks. For the asynchronous HARQ and time division du-plex (TDD) systems, the time interval is even larger. For clarity,in this paper we take the downlink synchronous HARQ of FDDsystems as a case study. Nevertheless, the same analysis canbe generalized to other cases as well. Moreover, to achieve acompromise between the system complexity and performance,

Fig. 2. Timing of the conventional HARQ scheme in C/U-plane decoupledrailway wireless networks.

chase combining in which retransmissions contain the sameset of coded bits as the initial transmission [13] is adoptedto combine the retransmitted data and the initially transmitteddata [14]–[16]. After each retransmission, the receiver usesmaximum ratio combination (MRC) to combine each receivedsignals and finally feeds them to the decoder.

Fig. 2 illustrates the timing of the conventional HARQscheme applied to C/U-plane decoupled railway wireless net-works. For clarity, we focus on the timing of one HARQprocess. In downlink, the small cell transmits the initial data (1)(denoted by D(1)) on subframe n. After decoding the receiveddata, the MR generates the corresponding acknowledgments.To guarantee the transmission reliability, the HARQ acknowl-edgments, as a kind of C-plane signaling, are kept at relativelyhigh-quality lower frequency bands in macro cells. In the situa-tion shown in Fig. 2, the data in the initial transmission are notcorrectly received. Thus, the MR generates an NACK and sendsit to the macro cell on subframe (n+ 4). Then, the macro cellforwards this NACK to the small cell via X3. In considerationof the forwarding latency of X3 interfaces, the subsequentretransmission for these erroneously received data is performedon subframe (n+ 8 + �Td,max�). As shown in Fig. 2, tworetransmissions are performed before the data are successfullydecoded. For D(1), the total latency caused by retransmissionsis 2 × (8 + �Td,max�) = (16 + 2�Td,max�) ms. Compared tothe conventional networks in which the latency caused by tworetransmissions is 16 ms, 2�Td,max� ms extra latency is broughtin, aggravating the latency problem in HARQ especially forlatency-sensitive services. For clarity, the wireless transmissiondelay is neglected in Fig. 2. Therefore, the subframes, on whichthe same data are transmitted and received, are aligned in thetime domain.

III. PROPOSED COLLABORATIVE HARQ SCHEME

In the above section, the aggravated retransmission la-tency problem of the conventional HARQ scheme working inC/U-plane decoupled railway wireless networks is discussed. Tomitigate the problem, the principle and timing of the proposedcollaborative HARQ scheme are presented in this section.

A. Principle of the Collaborative HARQ Scheme

Due to the change in C/U-plane decoupled railway wirelessnetworks where the whole lower frequency bands of macro


Fig. 3. (a) Principle of the proposed collaborative HARQ scheme forC/U-plane decoupled railway wireless networks. (b) Timing of the proposedscheme.

cells are used for C-plane transmissions, there may be sparespectrum resources on these high-quality bands. Suppose thatthe bandwidth of a macro cell is 10 MHz corresponding to 8400available resource elements (REs) in 1 ms, and 30 percent of1000 users in a train are active and scheduled in a frame of10 ms. To make a compromise, two control channel elements(CCEs), consisting of 72REs are assigned to the physical down-link control channel (PDCCH) of a user, and every eight usersshare a physical HARQ indicator channel (PHICH) as in con-ventional LTE networks. Then, the total consumed resources bycontrol channels and reference signals in 1 ms are 3008REs andthere are still 5392REs unused.

Based on this observation, to mitigate the aforementionedretransmission latency problem, a low-latency collaborativeHARQ scheme that exploits the possible spare resources inmacro cells to help small cells handle retransmissions is pro-posed, as shown in Fig. 3(a). Considering the large signalpropagation difference between discontinuous higher and lowerfrequency bands, if necessary, two dedicated antennas andreceiving circuits are integrated at the MR side to individuallyhandle the radio frequency (RF) signals received from macrocells and small cells. Obviously, compared to the conventionalnetwork architecture, although the C/U-plane decoupled net-work architecture can greatly increase the system capacity, itcomes at the expense of higher hardware complexity. Afterconverting RF signals to baseband signals, the receiving circuits

output the two parallel baseband signals of a retransmissionto the demodulators. Then, through chase combining, the twodemodulated bit streams are combined with the initial transmis-sion stored in the buffer memory. Finally, the combined signalsare fed to the decoder for a new decoding attempt.

B. Timing of the Collaborative HARQ Scheme

Correspondingly, the downlink timing of the proposed col-laborative HARQ scheme is depicted in Fig. 3(b). After re-ceiving an NACK on subframe (n+ 4), which is the HARQacknowledgment to the initially transmitted D(1) on subframen,the macro cell forwards it to the small cell via X3, resulting in amaximum Td,max latency. If there are spare spectrum resourcesin the macro cell, the small cell will forward the retransmitteddata to the macro cell via X3. Similarly, a maximum Td,max la-tency is induced again. As a case study, under the same situationas depicted in Fig. 2, in the proposed scheme the data are cor-rectly decoded after one retransmission which actually includesdouble copies of the retransmitted data. The latency of a retrans-mission with double copies of data concurrently transmitted inthe proposed scheme is (8 + 2�Td,max�) ms. Compared to theconventional scheme shown in Fig. 2, under the same situation,the total latency is reduced by 8 ms in the proposed scheme.When D(1) is correctly decoded, the MR feeds back an ACKto the macro cell on the subsequent subframe after 4 ms. Then,with a maximum Td,max latency, the acknowledgment is furtherforwarded to the small cell. As it is an ACK, the small celldirectly performs another new data transmission on subframe(n+ 16 + 3�Td,max�) without the need to forward data to themacro cell any more. Based on the above analysis, we canfigure out the timing between two adjacent (re)transmissionsin the proposed collaborative HARQ scheme. With respect toa retransmission, the time interval between this retransmissionand the previous (re)transmission is (8 + 2�Td,max�) ms. Thetime interval between a new data transmission and the previ-ous (re)transmission is (8 + �Td,max�) ms. According to thesetiming, the receiver can receive all data in sequence accurately.

IV. PROPOSED COLLABORATIVE

TRANSMISSION FRAMEWORK

Different from the conventional network architecture,C-plane and U-plane in the C/U-plane decoupled wirelessnetwork architecture are completely separated into differentnetwork nodes. Therefore, channel mappings need to be re-designed. In this paper, we take LTE protocols as a designbenchmark. As shown in Fig. 4, in the newly redesignedchannel mapping method, all control channels are kept at macrocells, and all traffic channels are moved to small cells. In macrocells, a new MAC uplink (or downlink) control channel (i.e.,U(D)L-CCH) is defined to carry some of up-layer RLC controlchannels, which is finally mapped to a converged physicaluplink (or downlink) control channel (CPU(D)CCH). In smallcells, a new MAC traffic channel, uplink (or downlink) trafficchannel (U(D)L-TCH), is defined and finally mapped to aphysical uplink (or downlink) traffic channel (PU(D)TCH). Interms of physical resources, all C-plane channels are eventuallymapped to lower frequency bands, and all U-plane channels


Fig. 4. Collaborative transmission framework.

are mapped to higher frequency bands. Therefore, the physicalcontrol format indicator channel (PCFICH) in the conventionalcoupled LTE networks, which is used to discriminate theboundary of the control and traffic channels sharing the samefrequency bands, is saved in the C/U-plane decoupled networkarchitecture.

To realize collaborative transmissions between two differentnetwork nodes, i.e., macro cells and small cells, new peerentities, namely, collaborative transmission entities (CTEs) areproposed to be deployed in the MAC layers of macro cells andsmall cells. Through an X3 interface, the CTEs in different basestations can communicate with each other. Note that only thepotential spare resources in collaborative transmissions macrocells are exploited to help transmit U-plane data of small cells.The real control of these U-plane data transmissions, includingHARQ decisions, is still under the control of small cells.Therefore, as shown Fig. 4, the forwarded U-plane MAC PDUsfrom small cells are directly mapped to physical resourcesof macro cells without going through the HARQ module ofmacro cells. After receiving the data, MRs will send the cor-responding HARQ acknowledgements contained in PHICH onmore dependable lower frequency bands, and then they areforwarded by macro cells to small cells. Finally, based on thisinformation, small cells make decisions for the forthcomingtransmissions. For clarity, the whole collaborative transmissionprocess consists of the following five steps:

Step 1: In the macro cell, its MAC controller periodicallyinforms its CTE of the resource usage of lowerfrequency bands.

Step 2: Via X3, the resource usage of the macro cell isforwarded by its CTE to the CTE of the small cell.

Step 3: If there are spare spectrum resources in the macrocell, the MAC controller of the small cell will transfersome data to its own CTE.

Step 4: The CTE of the small cell forwards these data to theCTE of the macro cell. Then, based on the currentsystem states, the MAC controller of the macro cellmakes a decision on the resources and transmissionformats used for collaborative transmissions.

Step 5: With the help of the macro cell, the U-plane data canbe transmitted on both lower and higher frequencybands, enhancing the spectrum utilization of lowerfrequency bands. After receiving the data, MRs willfeed back HARQ acknowledgements contained inPHICH on more dependable lower frequency bands.

Then, macro cells forward these acknowledgementsto small cells via X3, based on which small cellsmake decisions for the following transmissions.

Moreover, as shown in Fig. 4, in the macro cell, a new MACchannel, namely, collaborative transmission channel (CTCH)and a new PHY channel, namely, physical collaborative trans-mission channel (PCTCH) are brought in to accommodatecollaborative transmissions. To instruct MRs to precisely re-ceive data in the framework, the message indicating whethera collaborative transmission is active or not and the resourcesas well as the transmission formats used for transmissionsin macro cells and small cells is carried by PDCCHs. Fromthe physical resource point of view, the proposed frameworkequivalently establishes a virtual bridge between completelydiscontinuous lower and higher frequency bands, and thusenhancing the flexibility of bandwidth extension for C/U-planedecoupled railway wireless networks. Considering the generalapplicability, the framework is described from a more generalperspective above. Although the system capacity can be in-tuitively increased if the possible spare resources are used totransmit the general U-plane data, for broadband C/U-planedecoupled railway wireless networks the capacity is not a keyproblem temporarily. Nevertheless, as what will be shown inSection VI, if they are used to help retransmissions, the aver-age retransmission latency can be highly reduced. Therefore,to mitigate the latency problem, in this paper we use thiscollaborative transmission framework to support collaborativeretransmissions between macro cells and small cells. That is,the forwarded data by small cells are retransmitted data, andthey are mapped on both higher frequency bands and lowerfrequency bands in duplication. It is also notable that if thereis no spare spectrum resource in macro cells, the system willdegenerate to the conventional scheme as shown in Fig. 2.

V. ANALYTICAL MODELS

In this section, we first describe the wireless channel ofhigh-speed railway scenarios. Then, theoretical analysis of theaverage number of retransmissions related to the sum of inde-pendent Gamma variables is conducted for the conventional andproposed schemes.

A. Wireless Channel Modeling

Doppler effect in the high-speed movement scenarios is a se-vere hindrance to high performance transmissions. Fortunately,in the special railway scenarios, the characteristics of deter-mined running directions, regular running tracks and repetitivemovements of trains along fixed running tracks lead to a regular,repetitive and predictable Doppler shift curve, thereby makingit easier to trace and compensate the Doppler effect under thisscenario [17]. Moreover, there have been many research studiesfocusing on the Doppler effect estimation and compensation forhigh-speed railway scenarios, such as in [18], and [19]. Basedon this observation, in this paper we assume that the Dopplereffect can be perfectly compensated and has almost no influenceon the final performance for both the conventional scheme andthe proposed scheme, which also ensures the fairness when


Fig. 5. Geometric sketch for the theoretical analysis.

comparing the performance of two schemes in both theoreticalanalysis and simulation experiments.

For high-speed railway scenarios, the most typical terrainis viaduct, in which wireless channels can be approximatedas line of sight (LOS) following a Rician distribution [20],[21]. To study the combining performance of (re)transmissions,we need to derive the joint probability density function (PDF)and cumulative distribution function (CDF) of multiple Ricianvariables. However, according to [22], it is almost impossibleto obtain an exact analytical joint PDF or CDF for more thanthree Rician variables. Fortunately, it is widely reported thatNakagami statistics can closely approximate Rician statisticswith a relationship between the Rician parameter K andNakagami parameter m as [23], [24]

m =(K + 1)2

(2K + 1). (1)

Under the Nakagami model, the received signal tonoise ratio (SNR) follows a Gamma distribution, i.e., γ ∼Gamma(m,m/γ), of which the PDF can be expressed as

fγ(γ) =

(m

γ

)mγm−1

Γ(m)e−mγ/γ · S(γ) (2)

where S(γ) is a unit step function and is defined as

S(γ) =

{1, γ > 0

0, otherwise(3)

and γ denotes the average received large-scale SNR, i.e.,γ = E[γ], where E[·] is the expectation operator. Fig. 5 de-scribes the geometric sketch to calculate the average large-scaleSNR of received signals from macro cells and small cells inC/U-plane decoupled railway wireless networks. In considera-tion of the linear topology of wireless communication networksin railway scenarios, the macro cells and small cells in Fig. 5are deployed on a straight line with vertical distance of dmin

to the rail. Rs, Rm and as denote the radius of a macro cell,the radius of a small cell and the overlapping distance of smallcells, respectively. To clarify the analysis, only one macro cellis considered in this paper, i.e., the analysis scope of d is fromas to 2Rm − as. Since macro cells and small cells operate atdifferent frequency bands with different characteristics such asdifferent coverage radiuses, for clarity we use the subscript mand s to represent the parameters of macro cells and small cells,respectively.

As shown in Fig. 5, suppose that the train starts from theoriginal point and travels through distance of d along theabscissa-axis direction, then the signal propagation distance,xm(d), from the macro cell to the train is

xm(d) =√(d−Rm)2 + d2min. (4)

TABLE IDESCRIPTIONS OF MCS MODES

Similarly, the signal propagation distance, xs(d), from thecurrent serving small cell to the train is

xs(d) =

√(d−Dis ·

⌊d

Dis

⌋− Dis

2

)2

+ d2min (5)

where Dis = 2Rs − as is defined to simplify the expression ofEq. (5).

Generally, the average received large-scale SNR can becalculated as

γ(x) =Pt · PL(x)

N0(6)

where Pt is the transmit power, PL(x) is the large-scale pathloss, and N0 is the noise power. Then, the average large-scaleSNR of received signals from the macro cell and the currentserving small cell can be separately expressed as

γm(xm) =Pm,t · PLm(xm)

N0(7)

γs(xs) =Ps,t · PLs(xs)

N0. (8)

Based on [25], for a given modulation and coding scheme(MCS) i, the packet error rate (PER) related to the instanta-neous SNR can be approximated as

Fi(γ) ≈{

1, if γ < γthi

ai exp(−giγ), if γ > γthi

(9)

where ai, gi, and γthi are three parameters determined by MCS

i as listed in Table I [25], [26].

B. Theoretical Analysis of the Conventional HARQ Scheme

To make the analysis more understandable, the effects ofincorrect receiving or losing of HARQ acknowledgments onthe overall performance are not considered. Let N con

max denotethe maximum number of permissible retransmissions for theconventional HARQ scheme in C/U-plane decoupled railwaywireless networks. Since in the conventional HARQ schemesmall cells perform all initial transmissions and retransmis-sions, for MCS is where is ∈ {1, 2, 3}, the average number ofrequired retransmissions of the conventional scheme, excludingthe initial transmission, can be derived as

Lis,con = E

⎡⎣Ncon

max∑n=1

n−1∏�=0

Fis

⎛⎝ �∑

j=0

γs,j

⎞⎠⎤⎦ (10)


where γs,0 is the received SNR of the initial transmission inthe small cell. The detailed derivation of Eq. (10) is given inAppendix A.

Suppose that the velocity of the train is v = 360 km/h andthe center frequency of small cells is fs = 5 GHz. Then, wecan get the maximum Doppler Shift in small cells as fd,s =vfs/c = 1.67 kHz, where c is the light speed. Correspond-ingly, the coherence time of wireless channels in small cellsis Tc,s = 0.423/fd,s = 0.25 ms [27], which is much shorterthan the time interval between two adjacent (re)transmissionsof an HARQ process. Thus, it is reasonable to assume that the(re)transmissions of an HARQ process experience independentwireless channels. Additionally, taking LTE networks as theanalysis baseline, the value of N con

max is 6 [28], and then thetime interval between the initial transmission and the sixthretransmission is (48 + 6�Td,max�) ms. Based on the field testresults in [12], let Td,max = 6 ms. And then 48 + 6�Td,max� =84 ms. During the time interval of 84 ms, the running distanceof the train is 8.4 m, which is relatively much shorter thanthe distance between base stations and the rail. Therefore,all (re)transmissions in an HARQ process can be assumed tohave the same average large-scale SNR. As a result, γs,j withj = 0, 1, 2 . . . in Eq. (10) follows an independent and identicaldistribution. According to [29], we can getΥs,� =

∑�j=0 γs,j ∼

Gamma((� + 1)ms,ms/γs). Therefore, the average numberof retransmissions of the conventional HARQ scheme inC/U-plane decoupled railway wireless networks can berewritten as

Lis,con

=

Nconmax∑

n=1

n−1∏�=0

⎛⎝Γlow

(msγ

this

γs, (�+1)ms

)Γ ((�+1)ms)

+ais

(1+gis

γs

ms

)−(�+1)ms

×

⎛⎝1−

Γlow

((ms

γs+gis

)γthis, (�+1)ms

)Γ ((�+1)ms)

⎞⎠⎞⎠

(11)

where Γlow(y,m) is the lower incomplete Gamma function, de-fined as Γlow(y,m) =

∫ y

0 xm−1e−xdx. The detailed derivationof Eq. (11) is given in Appendix A.

With the obtained average number of retransmissions, theaverage latency caused by retransmissions of the conventionalHARQ scheme in C/U-plane decoupled railway wireless net-works can be expressed as

Dcon = (8 + �Td,max�)Lis,con. (12)

In the conventional HARQ scheme, only a copy of thedata that are unsuccessfully decoded in the initial transmissionis carried in a retransmission. Accordingly, only a copy ofresource is consumed in a retransmission. For MCS is, afterLis,con retransmissions, the average system transmission rate is

Ris,con =Ris

Lis,con + 1. (13)

C. Theoretical Analysis of the Proposed CollaborativeHARQ Scheme

In the proposed collaborative HARQ scheme, initial trans-missions are carried by small cells, and the following retrans-missions will be collaboratively accomplished by small cellsand macro cells. Due to the differences of signal propagationcharacteristics on lower and higher frequency bands, for thetrain at the same geographic location as shown in Fig. 5, theaverage large-scale SNR of received signals from macro cellsand small cells may be different. Hence, the macro cell andsmall cell probably choose different MCS for the two copies ofdata in a single retransmission based on the assumption that theadaptive modulation and coding (AMC) technique is used. Inthis case, we cannot obtain the exact analytical expression of theaverage number of retransmissions for the proposed scheme.Nevertheless, based on the MCS with a higher order among thetwo MCSs selected by the macro cell and small cell, the upperlimit of the average number of required retransmissions canbe obtained for the proposed scheme. Similarly, based on theMCS with a lower order, the lower limit of the average numberof required retransmissions can be derived. Let im denote theselected MCS by the macro cell, where im ∈ {1, 2, 3}. As listedin Table I, the lower the values of is and im are, the lower theorder of MCSs is. With the definition of x = max(im, is), theupper limit of the average number of required retransmissionsin the proposed collaborative HARQ scheme is obtained as

Lpro ≤ E

⎡⎣Fis(γs,0) +

Npromax∑

n=2

Fis(γs,0)

×n−1∏�=1

Fx

⎛⎝ �∑

j=0

γs,j +

�∑j=1

γm,j

⎞⎠⎤⎦ . (14)

The detailed derivation of Eq. (14) is given in Appendix B. Forclarity, we separately conduct the derivation for each item inEq. (14). Based on the above analysis, we can obtain

E [Fis(γs,0)] =P(γs,0 < γth

is

)+ aise

−gisγs,0P(γs,0 > γth

is

)=

Γlow

(msγ

this

γs,ms

)Γ(ms)

+ ais

(1 + gis

γs

ms

)−ms

×(

1 −Γlow

((ms/γs + gis) γ

this,ms

)Γ(ms)

).

(15)

Similarly, suppose that the frequency center of macro cells isfm = 2 GHz. Then, the coherence time of wireless channelsin macro cells is Tc,m = 0.423/(vfm/c) = 0.63 ms, whichis much shorter than the time interval between two adja-cent (re)transmissions in the proposed scheme. Therefore,we can assume that the wireless channels experienced by(re)transmissions of an HARQ process in the macro cell areindependent on each other. Let Td,max = 6 ms. Consideringthat double copies of data are concurrently transmitted in aretransmission in the proposed scheme, the maximum numberof permissible retransmissions of the proposed scheme is set


to Npromax = 3. Then, the time interval between the initial trans-

mission and the third retransmission is 3 × (8 + 2�Td,max�) =60 ms. During this period, the running distance of the train is6 m, which is relatively much smaller than the distance betweenbase stations and the rail. Hence, the average large-scale SNR ofall (re)transmissions in an HARQ process is almost equivalent.As a consequence, it can be assumed that wireless channelsexperienced by all (re)transmissions of an HARQ process inthe macro cell follow an independent and identical distribution.Then,

Υs,� =

�∑j=0

γs,j ∼ Gamma

((� + 1)ms,

ms

γs

)

Υm,� =

�∑j=1

γm,j ∼ Gamma

(�mm,

mm

γm

). (16)

For clarity, we define

αs,� =(�+ 1)ms,1βs

=ms

γs

αm,� = �mm,1βm

=mm

γm

. (17)

As macro cells and small cells operate at completely differentfrequency bands, we can assume that transmissions in macrocells and small cells are diverse and independent. That is, Υs,�

and Υm,� are two independent Gamma variables with differentparameters. According to [30], [31], the PDF of the sum of thetwo variables, denoted by Y = Υs,� +Υm,�, can be derived as

g(y) =

(C

∞∑υ=0

δυyρ+υ−1e−y/βq

Γ(ρ+ υ)βρ+υq

)· S(y) (18)

where q, C, ρ and δ are interim coefficients to simplify theexpression of Eq. (18), and

q = minq∈{s,m}

(βs, βm)

C =

(βq

β{s,m}−q

)α{s,m}−q,�

ρ =αs,� + αm,�⎧⎨⎩δυ+1 = 1

υ+1

υ+1∑κ=1

α{s,m}−q,�

(1 − βq

β{s,m}−q

)κ

δυ+1−κ

δ0 = 1.(19)

Then, we can obtain the expectation of the last item inEq. (14) as

E

⎡⎣Fx

⎛⎝ �∑

j=0

γs,j +�∑

j=1

γm,j

⎞⎠⎤⎦

= C

∞∑υ=0

δυ

(Γlow

(γthx /βq, ρ+ υ

)Γ(ρ+ υ)

+ ax(1 + gxβq)−(ρ+υ)

×(

1 −Γlow

((1/βq + gx)γ

thx , ρ+ υ

)Γ(ρ+ υ)

)).

(20)

Considering the practical application, we take the first Ω itemsof the infinite series in Eq. (20) as an approximation, that is,

E

⎡⎣Fx

⎛⎝ �∑

j=0

γs,j +

�∑j=1

γm,j

⎞⎠⎤⎦

≈ C

Ω∑υ=0

δυ

⎛⎝Γlow

(γthx

βq, ρ+ υ

)Γ(ρ+ υ)


×(

1 −Γlow

((1/βq + gx)γ

thx , ρ+ υ

)Γ(ρ+ υ)

)⎞⎠.

(21)

To substitute the above results into Eq. (14), the upper limitof the average number of retransmissions in the proposed col-laborative HARQ scheme, denoted by L

upperpro , can be rewritten

as Eq. (22), shown at the bottom of the page. Similarly, if wedefine z = min(im, is), the lower limit of the average numberof required retransmissions in the proposed scheme, denoted by

Llowerpro , can be obtained as Eq. (23), shown at the bottom of the

next page.With the above results, the scope of the latency caused by

retransmissions in the proposed scheme is

(8 + 2�Td,max�)Llowerpro ≤ Dpro ≤ (8 + 2�Td,max�)L

upperpro .

(24)

In the proposed collaborative HARQ scheme, double copiesof data are concurrently transmitted in a retransmission, leadingto the consumption of double copies of resources. Therefore,

Lpro ≤ Lupperpro =

Γlow

(msγ

this/γs,ms

)Γ(ms)

+ ais

(1 + gis

γs

ms

)−ms

(1 −

Γlow

((ms/γs + gis) γ

this,ms

)Γ(ms)

)

+

Npromax∑

n=2

(Γlow

(msγ

this/γs,ms

)Γ(ms)

+ ais

(1 + gis

γs

ms

)−ms

(1 −

Γlow

((ms/γs + gis) γ

this,ms

)Γ(ms)

))

×n−1∏�=1

(C

Ω∑υ=0

δυ

(Γlow

(γthx /βq, ρ+ υ

)Γ(ρ+ υ)


(1 −

Γlow

((1/βq + gx)γ

thx , ρ+ υ

)Γ(ρ+ υ)

)))

(22)


the scope of the average system transmission rate in the pro-posed scheme is

Ris

2Lupperpro + 1

≤ Rpro ≤ Ris

2Llowerpro + 1

. (25)

VI. PERFORMANCE ANALYSIS AND COMPARISON

Based on the theoretical analyses in Section V, numericalresults are provided in this section to compare the performanceof the conventional and proposed schemes. Simulation exper-iments are performed under two conditions, i.e., under fixedMCS and under AMC. Due to the fact that AMC can enhancethe transmission reliability in some degree, the retransmissionlatency performance improvement of the proposed schemeunder AMC is less remarkable than that under fixed MCS.

A. Performance Comparisons Under Fixed MCS

In this section, to conduct fair and comprehensive per-formance comparisons, simulation experiments are performedunder the condition that the same MCS is used in small cellsand macro cells and is not adaptively changed when the trainruns through the whole wireless coverage. In this way, wecan investigate the pure performance improvements of theproposed scheme without the influence of AMC techniques onthe transmission reliability. Performance comparisons of theaverage number of retransmissions, the average retransmissionlatency and the average system transmission rate are illustratedin Figs. 6–8, respectively. Detailed simulation parameter set-tings are listed in Table II [4], [5]. For clarity, here two smallcells symmetrically located in the coverage of a macro cellare considered. Therefore, the following simulation results aresymmetrical to the position of the macro cell. For the purposeof performance analysis, we focus on the results of the left-handside as case studies.

As shown in Fig. 6, overall the proposed scheme requiresmuch fewer retransmissions compared to the conventionalscheme. Moreover, the higher the MCS order is, the moreremarkable the performance improvement of the proposedscheme is. For instance, under the MCS of 64QAM, when thetrain is at the edges of the macro cell which also correspondsto the edges of small cells, e.g., at d = 0.2 km, due to the lowSNR in these regions both schemes arrive at their maximumpermissible retransmissions. As the train moves towards thesmall cell, with double copies of data concurrently transmitted

Fig. 6. Performance comparisons of the average number of retransmissions fordifferent MCS modes.

Fig. 7. Performance comparisons of the average retransmission latency fordifferent MCS modes.

in a retransmission, the number of required retransmissionsof the proposed scheme is greatly reduced. For instance, atd = 0.3 km, the average numbers of retransmissions of theconventional scheme and the proposed scheme are 2 and 1,respectively. At the center areas of small cells in which the

Lpro ≥ Llowerpro =

Γlow

(msγ

this/γs,ms

)Γ(ms)

+ ais

(1 + gis

γs

ms

)−ms

(1 −

Γlow

((ms/γs + gis) γ

this,ms

)Γ(ms)

)

+

Npromax∑

n=2

(Γlow

(msγ

this/γs,ms

)Γ(ms)

+ ais

(1 + gis

γs

ms

)−ms

(1 −

Γlow

((ms/γs + gis) γ

this,ms

)Γ(ms)

))

×n−1∏�=1

(C

Ω∑υ=0

δυ

(Γlow

(γthz /βq, ρ+ υ

)Γ(ρ+ υ)

+ az(1 + gzβq)−(ρ+υ)

(1 −

Γlow

((1/βq + gz)γ

thz , ρ+ υ

)Γ(ρ+ υ)

)))

(23)


Fig. 8. Performance comparisons of the average system transmission rate fordifferent MCS modes.

TABLE IISIMULATION PARAMETERS

SNR of received signals from small cells is high, e.g., at d ∈(0.5, 0.7) km, the numbers of required retransmissions of bothschemes are close to zero. When the train is at the center areaof the macro cell which corresponds to the edges of these twosmall cells, thanks to the high SNR collaborative retransmis-sions from the macro cell, the performance improvement ofthe proposed scheme in this region is the most remarkable.At d = 1 km, the number of required retransmissions of theproposed scheme is about 1, while for the conventional schemeit reaches up to 6. For other MCSs, the whole trend is thesame as 64QAM. Nevertheless, because lower order MCSs canachieve higher retransmission reliability, as shown in Fig. 6, thelower the MCS order is, the less remarkable the performanceimprovement is.

Based on the above results, as shown in Fig. 7, with doublecopies of data concurrently transmitted in a retransmissionin the proposed scheme, to achieve the same transmissionreliability, the proposed scheme requires fewer retransmissions,thereby mitigating the latency problem caused by HARQ re-transmissions. For example, at d = 1 km, the average retrans-mission latency of 64QAM, 16QAM and QPSK is reduced bythe proposed scheme from about 84 ms to 14 ms, from about80 ms to 14 ms and from about 18 ms to 13 ms, respectively.

Also double copies of resources are consumed by a retransmis-sion in the proposed scheme. As depicted in Fig. 8, when thetrain is at the edges of the macro cell, the conventional schemeoutperforms the proposed scheme in terms of the averagesystem transmission rate. Nevertheless, with reduced retrans-missions in the proposed scheme, the performance gap betweentwo schemes is very small. On the contrary, for 16QAM and64QAM, at the center area of the macro cell, thanks to the highSNR collaborative retransmissions from the macro cell, muchfewer retransmissions are needed in the proposed scheme. Asaforementioned, at d = 1 km in Fig. 6, the proposed schemereduces the average number of required retransmissions fromabout 5.8 to 1 and from 6 to 1 for 16QAM and 64QAM, respec-tively. Therefore, in this region, the proposed scheme obtainsa higher average system transmission rate as shown in Fig. 8.Correspondingly, at d = 1 km, the performance improvementof the proposed scheme under 64QAM and 16QAM is about0.9 bit/symbols and 0.6 bit/symbols, respectively. However,as discussed above, for QPSK which has a higher ability inenhancing the transmission reliability, the performance im-provement of the average number of required retransmissionsis less remarkable. At d = 1 km of Fig. 6, the average numberof required retransmissions are reduced from about 1.3 to 0.9by the proposed scheme. Therefore, in Fig. 8, even at the centerarea of the macro cell, the conventional scheme still obtainsa higher average system transmission rate than the proposedscheme.

B. Performance Comparisons Under AMC

In practical wireless communication systems, AMC tech-niques are usually employed to adapt to various wireless chan-nels. If a wireless channel is of high quality, higher orderMCSs with higher transmission rate will be used to improvethe spectrum efficiency. Otherwise, lower order MCSs will beimplemented to enhance the transmission reliability. That isto say, AMC can enhance the transmission reliability in somedegree. Hence, under AMC, the performance improvement ofthe proposed scheme will not be very remarkable. To makethis more understandable, the MCS adaption results of themacro cell and small cell during the train running throughthe coverage of the macro cell are illustrated in Fig. 9. Thehigher the received signal quality is, the higher the MCS orderis selected. For the center areas of the macro cell and smallcells, the selected MCS mode is 64QAM. In contrast, QPSKis used for cell edges. And 16QAM is used for other areaswith intermediate signal quality. For simplicity, in this paper,we only consider the three MCSs listed in Table I, in which theSNR thresholds of MCS switching are given in the last row.Nevertheless, by substituting the corresponding MCS relatedparameters, the same analysis method also holds for other MCSs.

Fig. 10 depicts the average number of retransmissions of bothschemes under AMC, confirming the fact that the proposedscheme still outperforms the conventional scheme. Based onthe theoretical analysis, in the regions of d ∈ (0.2, 0.34) kmand d ∈ (0.72, 0.74) km where both the macro cell and smallcell adopt the same MCS as shown in Fig. 9, the obtainednumber of retransmissions of the proposed scheme in Fig. 10


Fig. 9. MCS adaptation results.

Fig. 10. Performance comparison of the average number of retransmissionsunder AMC.

are exact values, not the upper or lower limit. For other regions,as shown in Fig. 9, the macro cell and small cell always usedifferent MCSs. And we can only obtain the upper limit andlower limit of the average number of retransmissions in thoseregions for the proposed scheme. Besides, as shown in Fig. 9,when the train is in those regions, either the macro cell or thesmall cell can provide a high SNR retransmission. Therefore,in the proposed scheme which employs both the macro cell andsmall cell to handle retransmissions, for all MCSs, the numbersof required retransmissions are very low and the performancedifference among them is small. As a consequence, as shownin Fig. 10, the two curves of the upper limit and lower limit ofthe average number of retransmissions in the proposed schemeare almost overlapped. Then, in the following analysis, we canuse one of them as an approximate curve of the real averagenumber of retransmissions for the proposed scheme. Due tothe fact that AMC techniques can enhance the transmissionreliability in some degree, as shown in Fig. 10 the total numberof required retransmissions of both schemes are less than 1.5

Fig. 11. Performance comparisons of the average retransmission latency andaverage system transmission rate under AMC.

and the performance improvement of the proposed scheme isnot very remarkable.

Fig. 11 compares the average retransmission latency andthe average system transmission rate comparisons between twoschemes under AMC. In the proposed scheme, with doublecopies of data concurrently transmitted in a retransmission,the HARQ retransmission latency is reduced. Nevertheless,as aforementioned, due to the fact that AMC techniques canenhance the transmission reliability in some degree, the per-formance improvement is not very remarkable. As a kindof sacrifice, also with double copies of resources consumedin a retransmission, the proposed scheme has lower averagesystem transmission rate compared to the conventional scheme.However, the performance gap is very small. In addition,thanks to the concept of C-plane and U-plane decoupling whichdramatically expands the bandwidth, the system capacity inthis network is not a critical problem. On the contrary, it isvery important and necessary to mitigate the latency problemwhen linking the completely separated C-plane and U-plane indifferent network nodes, which is also the main goal of this paper.

Alternatively, excluding the spectrum resources used byC-plane transmissions, if there are still spare resources in macrocells, they can also be exploited to transmit general U-planedata via the proposed collaborative transmission framework.Based on this observation, in order to present a more compre-hensive performance study, in Fig. 12, the effective transmis-sion rates of spare resources of macro cells used in two differentcases, i.e., collaborative HARQ retransmissions and generaltransmissions, are compared. As shown in Fig. 12, for thecase that spare resources are used for HARQ retransmissions,in the regions of d ∈ (0.2, 0.5) km and d ∈ (0.7, 1) km theseresources are invested to repeatedly retransmit the receivederroneous packets, leading to a lower effective transmission ratein these regions compared to the case that these resources areused for general transmissions. Nevertheless, as demonstratedabove, with the help of these resources to handle retrans-missions, the retransmission latency is highly reduced. As a


Fig. 12. Performance comparison of the effective transmission rates of spareresources used in different situations.

matter of fact, this is very common for the field of wirelesscommunications where some performance is sacrificed for theimprovements of other performance. Fortunately, for broadbandC/U-plane decoupled railway wireless networks, the capacityis not a key problem temporarily. On the contrary, the aggra-vated retransmission latency problem in this network is morepronounced. Hence, it is more beneficial here to utilize thepossible spare high-quality resources of macro cells to handleretransmissions.

VII. CONCLUSION

The recently proposed C/U-plane decoupled railway wirelessnetworks aim to meet dramatically growing wireless accessdemands of train passengers as well as the reliable transmissionrequirements of train control systems. Although the wholesystem capacity is highly increased in this network with theU-plane moved to broadband higher frequency bands, howto mitigate the latency problem when linking the completelyseparated C-plane and U-plane in different physical nodes be-comes important, especially for HARQ protocols which requirefrequent interactions between the C-plane and U-plane. Toaddress this challenge, in this paper we have proposed a low-latency collaborative HARQ scheme, in which if there are sparespectrum resources in macro cells excluding those used byC-plane transmissions, they will be exploited to help small cellshandle retransmissions. To realize collaborative transmissionsbetween two different network nodes, i.e., macro cells andsmall cells, a novel collaborative transmission framework isproposed. Although the framework in this paper is used forHARQ retransmissions, it can also be developed for gen-eral collaborative transmissions to enhance the flexibility ofbandwidth extension for C/U-plane decoupled railway wirelessnetworks. Accordingly, the channel mapping is also redesignedto conform to this framework.

Both the theoretical analysis and simulation experimentsare conducted under two different conditions, i.e., with andwithout AMC. No matter under which condition, the proposed

scheme always outperforms the conventional scheme in termsof the average retransmission latency. Due to the fact thatAMC techniques can enhance the transmission reliability insome degree, under the condition with AMC, the averagesystem transmission rate of the proposed scheme is slightlylower than that of the conventional scheme. Nevertheless, forC/U-plane decoupled railway wireless networks in whichbroadband higher frequency bands are integrated, the systemcapacity is not a key point temporarily. In contrast, in this net-work, how to mitigate the aggravated latency during HARQ re-transmissions becomes important, which is exactly the researchfocus of this paper. As a matter of fact, in the field of wirelesscommunications, sacrificing some spectrum resources to gainthe transmission reliability is a common means. For our futurework, we will consider the differences of signal propagationcharacteristics on higher and lower frequency bands, such asdifferent Doppler shifts and frame structures when combiningthe data received from macro cells and small cells, so as tomake the collaborative transmission scheme more practical andfurther increase the data combining performance.

APPENDIX ADERIVATION OF EQUATIONS (10) AND (11)

Lis,con = Pr (Sus,1|Fas,0)+2Pr(Sus,2|Fas,0, Fas,1)+, . . . ,

+ (N conmax − 1) Pr

(Sus,Ncon

max−1 |Fas,0, Fas,1, . . . ,

Fas,Nconmax−2

)+N con

max

× Pr(Fas,0, Fas,1, . . . , Fas,Ncon

max−1

)=E

⎡⎣Ncon

max−1∑n=1

n

⎛⎝1 − Fis

⎛⎝ n∑

j=0

γs,j

⎞⎠⎞⎠

×n−1∏�=0

Fis

⎛⎝ �∑

j=0

γs,j

⎞⎠+N con

max

Nconmax−1∏�=0

Fis

⎛⎝ �∑

j=0

γs,j

⎞⎠⎤⎦

=E

⎡⎣Ncon

max∑n=1

n−1∏�=0

Fis

⎛⎝ �∑

j=0

γs,j

⎞⎠⎤⎦

=

Nconmax∑

n=1

n−1∏�=0

(P(Υs,�<γth

is

)+aise

−gisΥs,�P(Υs,�>γ

this

))

=

Nconmax∑

n=1

n−1∏�=0

⎛⎝Γlow

(msγ

this

γs, (�+ 1)ms

)Γ ((�+ 1)ms)

+ ais

×(

1 + gisγs

ms

)−(�+1)ms

×

⎛⎝1−Γlow

((ms

γs+gis

)γthis, (�+1)ms

)Γ ((�+1)ms)

⎞⎠⎞⎠

(26)

where Su indicates the event that data in this transmission aresuccessfully decoded, and Fa denotes the otherwise case. Thefirst three equations are the derivation steps of Eq. (10), and thelast two equations are the derivation steps of Eq. (11).


APPENDIX BDERIVATION OF EQUATION (14)

Lpro = Pr(Sum,s,1|Fas,0) + 2Pr(Sum,s,2|Fas,0, Fam,s,1)

+, . . . ,+(Npromax − 1) Pr

(Sum,s,Npro

max−1|Fas,0, . . . ,

Fam,s,Npromax−2

)+Npro

max Pr(Fas,0, Fam,s,1, . . . , Fam,s,Npro

max−1

)≤E

⎡⎣Npro

max−1∑n=2

n

⎛⎝1 − Fx

⎛⎝ n∑

j=0

γs,j +

n∑j=1

γm,j

⎞⎠⎞⎠

×Fis(γs,0)

n−1∏�=1

Fx

⎛⎝ �∑

j=0

γs,j +

�∑j=1

γm,j

⎞⎠

+

⎛⎝1 − Fx

⎛⎝ 1∑

j=0

γs,j + γm,1

⎞⎠⎞⎠ · Fis(γs,0)

+NpromaxFis(γs,0)

Npromax−1∏�=1

Fx

⎛⎝ �∑

j=0

γs,j+

�∑j=1

γm,j

⎞⎠⎤⎦

=E

⎡⎣Fis(γs,0) +

Npromax∑

n=2

Fis(γs,0)

×n−1∏�=1

Fx

⎛⎝ �∑

j=0

γs,j +

�∑j=1

γm,j

⎞⎠⎤⎦. (27)

REFERENCES

[1] X. Zhu, S. Chen, H. Hu, X. Su, and Y. Shi, “TDD-based mobile com-munication solutions for high-speed railway scenarios,” IEEE WirelessCommun., vol. 20, no. 6, pp. 22–29, Dec. 2013.

[2] B. Ai et al., “Challenges toward wireless communications for high-speedrailway,” IEEE Trans. Intell. Transp. Syst., vol. 15, no. 5, pp. 2143–2158,Oct. 2014.

[3] J. Calle-Sanchez, M. Molina-Garcia, J. I. Alonso, and A. Fernandez-Duran,“Long term evolution in high speed railway environments: Feasibility andchallenges,” Bell Labs Tech. J., vol. 18, no. 2, pp. 237–253, Sep. 2013.

[4] L. Yan, X. Fang, and Y. Fang, “Control and data signaling decoupledarchitecture for railway wireless networks,” IEEE Wireless Commun.,vol. 22, no. 1, pp. 103–111, Feb. 2015.

[5] L. Yan and X. Fang, “Reliability evaluation of 5G C/U-plane decou-pled architecture for high-speed railway,” EURASIP J. Wireless Commun.Netw., vol. 2014, pp. 1–11, 2014.

[6] C.-X. Wang et al., “Cellular architecture and key technologies for5G wireless communication networks,” IEEE Commun. Mag., vol. 52,no. 2, pp. 122–130, Feb. 2014.

[7] S. Ahmad and D. Datla, “Distributed power allocations in heterogeneousnetworks with dual connectivity using backhaul state information,” IEEETrans. Wireless Commun., vol. 14, no. 8, pp. 4574–4581, Aug. 2015.

[8] L. Lu, M. Xiao, and L. Rasmussen, “Relay-aided broadcasting with in-stantaneously decodable binary network codes,” in Proc. IEEE ICCCN,Maui, HI, USA, Jul. 2011, pp. 1–5.

[9] M. Xiao and M. Skoglund, “Multiple-user cooperative communicationsbased on linear network coding,” IEEE Trans. Commun., vol. 58, no. 12,pp. 3345–3351, Dec. 2010.

[10] L. Lu, M. Xiao, L. Rasmussen, and M. Skoglund, “Efficient schedulingfor relay-aided broadcasting with random network codes,” in Proc. IEEEPIMRC, Toronto, ON, Canada, Sep. 2011, pp. 1815–1819.

[11] E. Dahlman, S. Parkvall, and J. Sköld,LTE/LTE-Advanced for MobileBroadband. Amsterdam, The Netherlands: Elsevier, 2011.

[12] L. Zhang, Y. Nagai, T. Okamawari, and T. Fujii, “Field experiment ofnetwork control architecture for CoMP JT in LTE-advanced over asyn-chronous X2 interface,” in Proc. IEEE 77th VTC—Spring, Dresden,Germany, Jun. 2013, pp. 1–5.

[13] D. Chase, “Code combining—A maximum-likelihood decoding approachfor combining an arbitrary number of noisy packets,” IEEE Trans.Commun., vol. 33, no. 5, pp. 385–393, May 1985.

[14] P. Frenger, S. Parkvall, and E. Dahlman, “Performance comparison ofHARQ with chase combining and incremental redundancy for HSDPA,”in Proc. IEEE 54th Veh. Technol. Conf., Atlantic City, NJ, USA, 2001,vol. 3, pp. 1829–1833.

[15] “Performance comparison of Hybrid-ARQ schemes,” Motorola,Stockholm, Sweden, TSG R1-17-00-1396, 3GPP Input Paper, 2000.

[16] K. C. Beh, A. Doufexi, and S. Armour, “Performance evaluation of hybridARQ schemes of 3GPP LTE OFDMA system,” in Proc. IEEE 18th Int.Symp. PIMRC, Athens, Greece, Sep. 2007, pp. 1–5.

[17] Y. Zhao, C. Yin, and J. Li, “Learning- and optimization-based channelestimation for cognitive high-speed rail broadband wireless communi-cations,” in Proc. IEEE ISCIT , Gold Coast, Qld., Australia, Oct. 2012,pp. 562–567.

[18] A. Kalakech, M. Berbineau, I. Dayoub, and E. Simon, “Time domainLMMSE channel estimator based on sliding window for OFDM systemsin high mobility situations,” IEEE Trans. Veh. Technol., vol. 64, no. 12,pp. 5728–5740, Dec. 2015.

[19] Q. Du, G. Wu, Q. Yu, and S. Li, “ICI mitigation by Doppler frequencyshift estimation and pre-compensation in LTE-R systems,” in Proc. IEEEICCC, Beijing, China, Aug. 2012, pp. 469–474.

[20] L. Liu et al., “Position-based modeling for wireless channel on high-speed railway under a viaduct at 2.35 GHz,” IEEE J. Sel. Areas Commun.,vol. 30, no. 4, pp. 834–845, May 2012.

[21] W. Luo, X. Fang, M. Cheng, and Y. Zhao, “Efficient Multiple-GroupMultiple-Antenna (MGMA) scheme for high-speed railway viaducts,”IEEE Trans. Veh. Technol., vol. 62, no. 6, pp. 2558–2569, Jul. 2013.

[22] P. Dharmawansa, N. Rajatheva, and C. Tellambura, “On the trivariate Ri-cian distribution,” IEEE Trans. Commun., vol. 56, no. 12, pp. 1993–1997,Dec. 2008.

[23] M. Yacoub, M. Barbin, M. de Castro, and J. B. Vargas, “Level crossingrate of Nakagami-m fading signal: Field trials and validation,” Electron.Lett., vol. 36, no. 4, pp. 355–357, Feb. 2000.

[24] J. Proakis,Digital Communications, 4th ed. New York, NY, USA:McGraw-Hill, 2000.

[25] H. Jin, C. Cho, N.-O. Song, and D. K. Sung, “Optimal rate selection forpersistent scheduling with HARQ in time-correlated Nakagami-m fadingchannels,” IEEE Trans. Wireless Commun., vol. 10, no. 2, pp. 637–647,Feb. 2011.

[26] J. Francis and N. Mehta, “EESM-based link adaptation in OFDM: Mod-eling and analysis,” in Proc. IEEE GLOBECOM, Atlanta, GA, USA,Dec. 2013, pp. 3703–3708.

[27] T. S. Rappaport,Wireless Communications: Principles and Practice.Upper Saddle River, NJ, USA: Prentice-Hall, 1999.

[28] W. Luo, X. Fang, S. Li, and Y. Xia, “Position assisted coordinate HARQin LTE systems for high speed railway,” in Proc. IEEE 77th VTC—Spring,Dresden, Germany, Jun. 2013, pp. 1–5.

[29] S. Kotz and J. W. Adams, “Distribution of sum of identically distributedexponentially correlated gamma-variables,” Ann. Math. Statist., vol. 35,no. 1, pp. 277–283, Mar. 1964.

[30] P. G. Moschopoulos, “The distribution of the sum of independent gammarandom variables,” Ann. Inst. Statist. Math., A, vol. 37, pp. 541–544,Mar. 1985.

[31] M.-S. Alouini, A. Abdi, and M. Kaveh, “Sum of gamma variates andperformance of wireless communication systems over Nakagami-fadingchannels,” IEEE Trans. Veh. Technol., vol. 50, no. 6, pp. 1471–1480,Nov. 2001.

Li Yan (S’14) received the B.E. degree in com-munication engineering from Southwest JiaotongUniversity, Chengdu, China, in 2012, where she iscurrently working toward the Ph.D. degree with theKey Laboratory of Information Coding and Transmis-sion, School of Information Science and Technology.Her research interests include handover, network ar-chitecture, and reliable wireless communication forhigh-speed railways.


Xuming Fang (M’00) received the B.E. degree inelectrical engineering, the M.E. degree in computerengineering, and the Ph.D. degree in communicationengineering from Southwest Jiaotong University,Chengdu, China, in 1984, 1989, and 1999, respec-tively. In September 1984, he was a Faculty Mem-ber with the Department of Electrical Engineering,Tongji University, Shanghai, China. He then joinedthe School of Information Science and Technology,Southwest Jiaotong University, where he has been aProfessor since 2001 and the Chair of the Depart-

ment of Communication Engineering since 2006. He held visiting positionswith the Institute of Railway Technology, Technical University at Berlin, Berlin,Germany, in 1998 and 1999 and with the Center for Advanced Telecommuni-cation Systems and Services, University of Texas at Dallas, Richardson, TX,USA, in 2000 and 2001. He has, to his credit, around 200 high-quality researchpapers in journals and conference publications. He has authored or coauthoredfive books or textbooks. His research interests include wireless broadbandaccess control, radio resource management, multihop relay networks, andbroadband wireless access for high-speed railway. Dr. Fang is the Chair of theIEEE Vehicular Technology Society of the Chengdu Chapter and an Editor ofthe IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.

Geyong Min (M’01) received the B.Sc. degree incomputer science from Huazhong University of Sci-ence and Technology, Wuhan, China, in 1995 andthe Ph.D. degree in computing science from theUniversity of Glasgow, Glasgow, U.K., in 2003.He is a Professor of high-performance computingand networking with the Department of Mathemat-ics and Computer Science, College of Engineering,Mathematics and Physical Sciences, University ofExeter, Exeter, U.K. His research interests includefuture Internet, computer networks, wireless commu-

nications, multimedia systems, high-performance computing, modeling, andperformance engineering.

Yuguang “Michael” Fang (F’08) received theB.S./M.S. degree from Qufu Normal University,Shandong, China, in 1987; the Ph.D. degree fromCase Western Reserve University, Cleveland, OH,USA, in 1994; and the Ph.D. degree from BostonUniversity, Boston, MA, USA, in 1997. In 2000, hejoined the Department of Electrical and ComputerEngineering, University of Florida, Gainesville, FL,USA, where he has been a Full Professor since 2005.He held a University of Florida Research Founda-tion Professorship from 2006 to 2009; a Changjiang

Scholar Chair Professorship with Xidian University, Xi’an, China, from 2008to 2011; and a Guest Chair Professorship with Tsinghua University, Beijing,China, from 2009 to 2012.

Dr. Fang received the U.S. National Science Foundation Career Award in2001 and the Office of Naval Research Young Investigator Award in 2002and was a recipient of the Best Paper Award from IEEE ICNP (2006). Hehas also received the 2010–2011 UF Doctoral Dissertation Advisor/MentoringAward, the 2011 Florida Blue Key/UF Homecoming Distinguished FacultyAward, and the 2009 UF College of Engineering Faculty Mentoring Award.He is the Editor-in-Chief of the IEEE TRANSACTIONS ON VEHICULAR

TECHNOLOGY, was the Editor-in-Chief of the IEEE TRANSACTIONS ONWIRELESS COMMUNICATIONS (2009–2012), and serves/served on the Ed-itorial Board of several journals, including the IEEE TRANSACTIONS ON

MOBILE COMPUTING (2003–2008, 2011–present), the IEEE TRANSACTIONS

ON COMMUNICATIONS (2000–2011), and the IEEE TRANSACTIONS ONWIRELESS COMMUNICATIONS (2002–2009). He has been actively partici-pating in conference organizations such as serving as the Technical ProgramCochair for IEEE INOFOCOM 2014 and the Technical Program Vice Chair forIEEE INFOCOM 2005.

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A Low-Latency Collaborative HARQ Scheme for Control/User ... · capability of mobile equipments, it is difﬁcult to overcome the severe challenges in high-speed railway scenarios,